Please explain how this is obvious. For one, I'm not sure the term "starship" would have been likely to mean otherwise to the production team at the time she was conceived, but I also don't see any particular reason why she can't carry out such a mission. It's certainly not because of the size difference. She's a little bigger than the TOS Enterprise and only 8% smaller than the movie version.
Right. I don't see why she wouldn't be a capable explorer. Personally, I just think the fact that it is designed differently implies that there were different goals in the two projects.
Here are some alternative possibilities: 1: The Enterprise in the 2280's was re-designated as a cadet training vessel while the old Republic was pulled out of service temporarily to be rebuilt to TMP-era specs. 2: The Reliant, Saratoga, et al are all starships-of-the-line, but they are not cruisers. Perhaps they are the TMP era's take on what FJ was trying to do when he came up with the Hermes/Saladin Class I destroyer/scout type vessels. Maybe the difference between a cruiser and a frigate/destroyer/scout/whatever-you-want-to-call-it is that cruisers have more overall mass, greater crew and cargo capacity, and separate, distinctive secondary hulls. Reliant obviously lacks these traits, so she may not have been a cruiser.
...But the Reliant does have mass/volume comparable to Kirk's ship, and seems to feature all the bells and whistles as well. She's just put together in a somewhat different shape. If the extremely subtle differences in size or equipment are indeed significant, then all bets are off as regards Starfleet ship type designations. Would for example the fandom Belknap qualify for a cruiser when her secondary hull is smaller than that of Kirk's ship, while her neck has greater chord? Is the Constellation not good enough for the cruiser designation due to the lack of a secondary hull, when she otherwise would seem to outbulk Kirk's ship by quite a lot? Timo Saloniemi
I'd argue that they're all types of cruisers, each designed with a specific purpose. The Constellation might be a Deep Space Cruiser, for example. The Miranda might be an Interdiction Cruiser. And the Constitution a good ole fashioned Heavy Cruiser. Of course, we might also want to factor in the idea that each class's mass might be different owing to different amounts of open space. Each of those hangar doors on the Miranda and Constellation might feature an empty volume similar to the one found aboard the Enterprise in TMP, making each of the former more hollow while still comparable in size.